A Linearithmic Time Locally Optimal Algorithm for the Multiway Number Partition Optimization

TL;DR

This paper introduces a linearithmic time algorithm for finding locally optimal solutions to the multiway number partition problem, which is NP-hard, providing a practical approach for large instances.

Contribution

The paper presents the first linearithmic time algorithm for locally optimal solutions in multiway number partitioning, improving efficiency over exponential-time methods.

Findings

Algorithm runs in O(N log N) time

Produces locally optimal solutions efficiently

Robust to various input types

Abstract

We study the problem of multiway number partition optimization, which has a myriad of applications in the decision, learning and optimization literature. Even though the original multiway partitioning problem is NP-hard and requires exponential time complexity algorithms; we formulate an easier optimization problem, where our goal is to find a solution that is locally optimal. We propose a linearithmic time complexity $O(N\log N)$ algorithm that can produce such a locally optimal solution. Our method is robust against the input and requires neither positive nor integer inputs.